Editing Werner Heisenberg (section)

===Matrix mechanics and the Nobel Prize===
{{more citations needed|section|date=February 2017}}
<!-- Deleted image removed: [[File:Bohr heisen pauli.jpg|thumb|[[Niels Bohr]], Werner Heisenberg, and [[Wolfgang Pauli]], c. 1935]] -->

Heisenberg's [[Umdeutung paper|''Umdeutung'' paper]] that established modern quantum mechanics<ref>{{cite journal|author=Heisenberg, W. |title=Über quantentheoretishe Umdeutung kinematisher und mechanischer Beziehungen|journal=Zeitschrift für Physik|volume=33|pages= 879–893|year= 1925|issue=1|doi=10.1007/BF01328377|bibcode=1925ZPhy...33..879H|s2cid=186238950}} (received 29 July 1925). [English translation in: B.L. van der Waerden, editor, ''Sources of Quantum Mechanics'' (Dover Publications, 1968) {{ISBN|978-0-486-61881-4}} (English title: "Quantum-Theoretical Re-interpretation of Kinematic and Mechanical Relations").]</ref>{{efn|name=old}} has puzzled physicists and historians. His methods assume that the reader is familiar with [[Hans Kramers|Kramers]]-Heisenberg transition probability calculations. The main new idea, [[Matrix multiplication#Properties of matrix multiplication|non-commuting matrices]], is justified only by a rejection of unobservable quantities. It introduces the non-[[Commutativity|commutative]] multiplication of [[Matrix (mathematics)|matrices]] by physical reasoning, based on the [[correspondence principle]], despite the fact that Heisenberg was not then familiar with the mathematical theory of matrices. The path leading to these results has been reconstructed by MacKinnon,<ref>{{cite journal |last=MacKinnon |first=Edward |title=Heisenberg, Models, and the Rise of Quantum Mechanics |journal=Historical Studies in the Physical Sciences |volume=8 |pages=137–188 |year=1977 |jstor=27757370 |doi=10.2307/27757370}}</ref> and the detailed calculations are worked out by Aitchison and coauthors.<ref>{{cite journal |last1=Aitchison |first1=Ian J.R. |first2=David A. |last2=MacManus |first3=Thomas M. |last3=Snyder |s2cid=53118117 |title=Understanding Heisenberg's 'magical' paper of July 1925: A new look at the calculational details |journal=American Journal of Physics |volume=72 |issue=11 |pages=1370–1379 |date=November 2004 |doi=10.1119/1.1775243 |arxiv=quant-ph/0404009v1|bibcode=2004AmJPh..72.1370A }}</ref>

In Copenhagen, Heisenberg and [[Hans Kramers]] collaborated on a paper on dispersion, or the scattering from atoms of radiation whose wavelength is larger than the atoms. They showed that the successful formula Kramers had developed earlier could not be based on Bohr orbits, because the transition frequencies are based on level spacings which are not constant. The frequencies which occur in the [[Fourier transform]] of the classical [[sharp series]] orbits, by contrast, are equally spaced. But these results could be explained by a semi-classical [[virtual state]] model: the incoming radiation excites the valence, or outer, electron to a virtual state from which it decays. In a subsequent paper, Heisenberg showed that this virtual oscillator model could also explain the polarization of fluorescent radiation.

These two successes, and the continuing failure of the [[Bohr model|Bohr–Sommerfeld model]] to explain the outstanding problem of the anomalous Zeeman effect, led Heisenberg to use the virtual oscillator model to try to calculate spectral frequencies. The method proved too difficult to immediately apply to realistic problems, so Heisenberg turned to a simpler example, the [[anharmonic oscillator]].

The dipole oscillator consists of a [[simple harmonic oscillator]], which is thought of as a [[charged particle]] on a spring, perturbed by an external force, like an external charge. The motion of the oscillating charge can be expressed as a [[Fourier series]] in the frequency of the oscillator. Heisenberg solved for the quantum behavior by two different methods. First, he treated the system with the virtual oscillator method, calculating the transitions between the levels that would be produced by the external source.

He then solved the same problem by treating the anharmonic potential term as a perturbation to the harmonic oscillator and using the [[Perturbation theory|perturbation methods]] that he and Born had developed. Both methods led to the same results for the first and the very complicated second-order correction terms. This suggested that behind the very complicated calculations lay a consistent scheme.

So Heisenberg set out to formulate these results without any explicit dependence on the virtual oscillator model. To do this, he replaced the Fourier expansions for the spatial coordinates with matrices, matrices which corresponded to the transition coefficients in the virtual oscillator method. He justified this replacement by an appeal to Bohr's correspondence principle and the Pauli doctrine that quantum mechanics must be limited to observables.

On 9 July, Heisenberg gave Born this paper to review and submit for publication. When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices,<ref>{{cite book |author-link=Abraham Pais |first=Abraham |last=Pais |title=Niels Bohr's Times in Physics, Philosophy, and Polity |publisher=Clarendon Press |year=1991 |isbn=978-0-19-852049-8 |pages=[https://archive.org/details/nielsbohrstimesi00pais_0/page/275 275–279] |url=https://archive.org/details/nielsbohrstimesi00pais_0/page/275 }}</ref> which he had learned from his study under [[Jakob Rosanes]]<ref>[http://nobelprize.org/nobel_prizes/physics/laureates/1954/born-lecture.pdf Max Born] {{Webarchive|url=https://web.archive.org/web/20121019194414/http://www.nobelprize.org/nobel_prizes/physics/laureates/1954/born-lecture.pdf |date=19 October 2012 }} ''The Statistical Interpretation of Quantum Mechanics'', Nobel Lecture (1954)</ref> at [[Breslau University]]. Born, with the help of his assistant and former student [[Pascual Jordan]], began immediately to make the transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg's paper.<ref>{{cite journal |first1=M. |last1=Born |first2=P. |last2=Jordan |s2cid=186114542 |title=Zur Quantenmechanik |journal=Zeitschrift für Physik |volume=34 |issue=1 |pages=858–888 |year=1925 |doi=10.1007/BF01328531 |bibcode=1925ZPhy...34..858B }} (received 27 September 1925). [English translation in: {{harvnb|van der Waerden|1968|loc=[https://books.google.com/books?id=8KLMGqnZCDcC&pg=PA277 "On Quantum Mechanics"]}}]</ref> A follow-on paper was submitted for publication before the end of the year by all three authors.<ref>{{cite journal |first1=M. |last1=Born |last2=Heisenberg |first2=W. |first3=P. |last3=Jordan |s2cid=186237037 |title=Zur Quantenmechanik II |journal=Zeitschrift für Physik |volume=35 |pages=557–615 |year=1925 |bibcode=1926ZPhy...35..557B |doi=10.1007/BF01379806 |issue=8–9 }} The paper was received on 16 November 1925. [English translation in: {{harvnb|van der Waerden|1968|loc=[https://books.google.com/books?id=8KLMGqnZCDcC&pg=PA321 15 "On Quantum Mechanics II"]}}]</ref>

Up until this time, matrices were seldom used by physicists; they were considered to belong to the realm of [[pure mathematics]]. [[Gustav Mie]] had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattice theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics.<ref>Jammer, Max (1966) ''The Conceptual Development of Quantum Mechanics''. McGraw-Hill. pp. 206–207.</ref>

In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the [[Nobel Prize in Physics]].<ref>{{harvnb|Bernstein| 2004|p= 1004}}</ref> The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933.<ref>{{cite book |last=Greenspan |first=Nancy Thorndike |title=[[The End of the Certain World|The End of the Certain World: The Life and Science of Max Born]] |publisher=Basic Books |year=2005 |isbn=978-0-7382-0693-6 |page=190}}</ref> It was at that time announced that Heisenberg had won the Prize for 1932 "for the creation of quantum mechanics, the application of which has, [[List of Latin phrases: I#inter alia|inter alia]], led to the discovery of the [[Spin isomers of hydrogen|allotropic forms of hydrogen]]".<ref name=nobelprize>[http://nobelprize.org/nobel_prizes/physics/laureates/1932/ The Nobel Prize in Physics 1932] {{Webarchive|url=https://web.archive.org/web/20080716011447/http://nobelprize.org/nobel_prizes/physics/laureates/1932/ |date=16 July 2008 }}. Nobelprize.org. Retrieved on 1 February 2012.</ref><ref name=ReferenceA>[[Nobel Prize in Physics]] and [http://nobelprize.org/nobel_prizes/physics/laureates/1933/press.html 1933] {{Webarchive|url=https://web.archive.org/web/20080715234807/http://nobelprize.org/nobel_prizes/physics/laureates/1933/press.html |date=15 July 2008 }}&nbsp;– Nobel Prize Presentation Speech.</ref>